Rota-Baxter operators with arbitrary weight (also called weighted Rota-Baxter operators) was considered in [1]}, [2]}. They are related with tridendriform algebras [3]}, post-Lie algebras and modified Yang-Baxter equations [2]}, weighted infinitesimal bialgebras and weighted Yang-Baxter equations [5]}, combinatorics of rooted forests [6]}, among others. Recently, the authors in [7]} defined the cohomology of Rota-Baxter operators of weight 1 on Lie algebras and Lie groups. This motivates the present author to study cohomology and deformations of weighted Rota-Baxter operators on both associative and Lie algebras [8]}. However, the simultaneous deformations of (associative) algebras and weighted Rota-Baxter operators are considered in a recent preprint of Wang and Zhou [9]}. More precisely, they considered weighted Rota-Baxter associative algebras and define cohomology of them with coefficients in a suitable Rota-Baxter bimodule. When considering the cohomology with coefficients in itself, it governs the simultaneous deformations of algebras and weighted Rota-Baxter operators.
